arXiv subjects

Benjamin P. Brown

Publications and source records attributed to Benjamin P. Brown.

At least 19 recordsLinked to original sources

arXiv2026

The Unsteady Taylor--Vortex Dynamo is Fast

Astrophysical and geophysical fluids commonly generate organized magnetic fields, despite having enormous magnetic Reynolds numbers $\rm{Rm}$ and abundant small-scale turbulence. Flow-induced dynamo action produces these fields, with the ``kinematic dynamo problem'' devoted to determining the rate at which a flow exponentially amplifies weak magnetic fields. However, previous studies on high-Rm kinematic dynamos have generated flows via imposed volumetric forcing or oscillatory boundary conditions. In this letter, we investigate a system with three important attributes: realistic flow conditions, fast dynamo action (operational for $\rm{Rm}\to\infty$), and a subharmonic spatio-temporal structure. We show that unsteady Taylor--vortex flow, a regime observed in laboratory experiments, gives rise to fast dynamos with time and length scales twice those of the flow at high $\rm{Rm}$. By numerically integrating a Floquet system driven by periodic oscillations of Taylor vortices, we solve the kinematic dynamo problem up to $\rm{Rm} = 3.2 \cdot 10^6$, calculating the dynamo's growth rate as a function of Rm and streamwise wavenumber. We find the onset of instability and compute Finite-Time Lyapunov Exponents, which identify the regions of Lagrangian chaos required for fast dynamo action. To our knowledge, unsteady Taylor--vortex flow produces the most physically motivated fast dynamo to date.

physics.flu-dyn↗

arXiv2025

Heat Transport and Dissipation in 2.5D Rotating Internally Heated and Cooled Convection

Models of astrophysical convection, such as mixing length theory, typically assume that the heat transport is independent of microphysical diffusivities. Such 'diffusion-free' behaviour is, however, not observed in numerical simulations employing standard fixed-flux or fixed-temperature boundary conditions, except possibly in extreme parameter regimes that are computationally expensive to achieve. Recent numerical and experimental work has suggested that internally heated and cooled convection can exhibit diffusion-free scalings in more numerically accessible regimes. Here, we present direct numerical simulations of 2.5D Cartesian rotating thermal convection driven by an internal heating and cooling function. The use of distributed heating and cooling functions alleviates sharp thermal boundary layers that would otherwise be present, allowing the flows to be simulated with modest computational resources. We show that for high Rossby numbers this set-up recovers mixing length theory scalings for the heat transport. The velocity amplitudes, in contrast, are observed to display diffusion-limited scalings. By comparing against boundary driven rotating convection, we show that internally heated cases have a larger fraction of their thermal dissipation occuring in the bulk of the fluid. We suggest this is connected to the increased convective efficiency observed in these cases. Our results indicate that 2.5D internally heated convection can be used as a computationally inexpensive test-bed to investigate some aspects of diffusion-free heat transport.

astro-ph.SR↗

arXiv2025

Rapidly Rotating Wall-Mode Convection

In the rapidly rotating limit, we derive a balanced set of reduced equations governing the strongly nonlinear development of the convective wall-mode instability in the interior of a general container. The model illustrates that wall-mode convection is a multiscale phenomenon where the dynamics of the bulk interior diagnostically determine the small-scale dynamics within Stewartson boundary layers at the sidewalls. The sidewall boundary layers feedback on the interior via a nonlinear lateral heat-flux boundary condition, providing a closed system. Outside the asymptotically thin boundary layer, the convective modes connect to a dynamical interior that maintains scales set by the domain geometry. In many ways, the final system of equations resembles boundary-forced planetary geostrophic baroclinic dynamics coupled with barotropic quasi-geostrophic vorticity. The reduced system contains the results from previous linear instability theory but captured in an elementary fashion, providing a new avenue for investigating wall-mode convection in the strongly nonlinear regime. We also derive the dominant Ekman-flux correction to the onset Rayleigh number for large Taylor number, $\textit{Ra} \approx 31.8 \,\textit{Ta}^{1/2} - 4.43 \,\textit{Ta}^{5/12} + \mathcal{O}(\textit{Ta}^{1/3})$ for no-slip boundaries. However, we find that the linear onset in a finite cylinder differs noticeably compared to a Cartesian channel. We demonstrate some of the reduced model's nonlinear dynamics with numerical simulations in a cylindrical container.

physics.flu-dyn↗

arXiv2025

Morphological Regimes of Rotating Moist Convection

Moist convection is a physical process where the latent heat released by condensation acts as a buoyancy source that can enhance or even trigger an overturning convective instability. Since the saturation temperature often decreases with height, condensation releases latent heat preferentially in regions of upflow. Due to this inhomogeneous heat source, moist convection may be more sensitive to changes in flow morphology, such as those induced by rotation, than dry Rayleigh-Bénard convection. In order to study the effects of rotation on flows driven by latent heat release, we present a suite of numerical simulations that solve the Rainy-Bénard equations (Vallis et al. 2019). We identify three morphological regimes: a cellular regime and a plume regime broadly analogous to those found in rotating Rayleigh Bénard convection, and a novel funnel regime that lacks a clear analog within the regimes exhibited by dry convection. We measure energy fluxes through the system and report rotational scalings of the Reynolds and moist Nusselt numbers. We find that moist static energy transport, as measured by a moist Nusselt number, is significantly enhanced in the funnel regime without a corresponding enhancement in Reynolds number, indicating that this funnel regime produces structures with more favorable correlations between the temperature and vertical velocity.

physics.flu-dyn↗

arXiv2025

3D Simulations Demonstrate Propagating Thermohaline Convection for Polluted White Dwarfs

Polluted white dwarfs (WDs) with small surface convection zones deposit significant concentrations of heavy elements to the underlying radiative interior, presumably driving thermohaline convection. Current models of polluted WDs frequently fail to account for this effect, although its inclusion can increase the inferred accretion rate by orders of magnitude. It has been argued that this instability cannot be treated as a continuous mixing process and thus should not be considered in these models. In this work, we study three-dimensional simulations of a thermohaline-unstable layer propagating into an underlying stable region, approximating the polluted WD scenario. We find that although thermohaline convection works to reduce driving gradients somewhat, the front continues to propagate and the system remains unstable. Importantly, the turbulent flux of metals broadly dominates over the diffusive flux in quantitative agreement with with existing mixing prescriptions implemented in some stellar evolution models (except slightly below the boundary of the propagating front, where recent prescriptions neglect overshoot-like effects). Thus, our results broadly support polluted WD models that include thermohaline mixing in their estimates of the settling rate.

astro-ph.SR↗

arXiv2025

On the Linear Stability of Partially and Fully Saturated Atmospheres to Moist Convection

We present a linear analysis of a minimal model of moist convection under a variety of atmospheric conditions. The stationary solutions that we analyze include both fully saturated and partially unsaturated atmospheres in both unconditionally and conditionally unstable cases. We find that all of the solutions we consider are linearly unstable via exchange of stability when sufficiently driven. The critical Rayleigh numbers vary by over an order of magnitude between unconditionally unstable and conditionally unstable atmospheres. The unsaturated atmospheres are notable for the presence of linear gravity wave-like oscillations even in unstable conditions. We study their eigenfunction structure and find that the buoyancy and moisture perturbations are anticorrelated in $z$, such that regions of negative buoyancy have positive moisture content. We suggest that these features in unsaturated atmospheres may explain the phenomenon of gravity wave shedding by moist convective plumes.

physics.flu-dyn↗

arXiv2024

Iterative Methods for Navier--Stokes Inverse Problems

Even when the partial differential equation underlying a physical process can be evolved forward in time, the retrospective (backward in time) inverse problem often has its own challenges and applications. Direct Adjoint Looping (DAL) is the defacto approach for solving retrospective inverse problems, but it has not been applied to deterministic retrospective Navier--Stokes inverse problems in 2D or 3D. In this paper, we demonstrate that DAL is ill-suited for solving retrospective 2D Navier--Stokes inverse problems. Alongside DAL, we study two other iterative methods: Simple Backward Integration (SBI) and the Quasi-Reversible Method (QRM). Our iterative SBI approach is novel while iterative QRM has previously been used. Using these three iterative methods, we solve two retrospective inverse problems: 1D Korteweg--de Vries--Burgers (decaying nonlinear wave) and 2D Navier--Stokes (unstratified Kelvin--Helmholtz vortex). In both cases, SBI and QRM reproduce the target final states more accurately and in fewer iterations than DAL. We attribute this performance gap to additional terms present in SBI and QRM's respective backward integrations which are absent in DAL.

physics.flu-dyn↗

arXiv2023

Internally heated and fully compressible convection: flow morphology and scaling laws

In stars and planets natural processes heat convective flows in the bulk of a convective region rather than at hard boundaries. By characterizing how convective dynamics are determined by the strength of an internal heating source we can gain insight into the processes driving astrophysical convection. Internally heated convection has been studied extensively in incompressible fluids, but the effects of stratification and compressibility have not been examined in detail. In this work, we study fully compressible convection driven by a spatially uniform heating source in 2D and 3D Cartesian, hydrodynamic simulations. We use a fixed temperature upper boundary condition which results in a system that is internally heated in the bulk and cooled at the top. We find that the flow speed, as measured by the Mach number, and turbulence, as measured by the Reynolds number, can be independently controlled by separately varying the characteristic temperature gradient from internal heating and the diffusivities. 2D simulations at a fixed Mach number (flow speed) demonstrate consistent power at low wavenumber as diffusivities are decreased. We observe convection where the velocity distribution is skewed towards cold, fast downflows, and that the flow speed is related to the length scale and entropy gradient of the upper boundary where the downflows are driven. We additionally find a heat transport scaling law which is consistent with prior incompressible work.

physics.flu-dyn↗

arXiv2023

The photometric variability of massive stars due to gravity waves excited by core convection

Massive stars die in catastrophic explosions, which seed the interstellar medium with heavy elements and produce neutron stars and black holes. Predictions of the explosion's character and the remnant mass depend on models of the star's evolutionary history. Models of massive star interiors can be empirically constrained by asteroseismic observations of gravity wave oscillations. Recent photometric observations reveal a ubiquitous red noise signal on massive main sequence stars; a hypothesized source of this noise is gravity waves driven by core convection. We present the first 3D simulations of massive star convection extending from the star's center to near its surface, with realistic stellar luminosities. Using these simulations, we make the first prediction of photometric variability due to convectively-driven gravity waves at the surfaces of massive stars, and find that gravity waves produce photometric variability of a lower amplitude and lower characteristic frequency than the observed red noise. We infer that the photometric signal of gravity waves excited by core convection is below the noise limit of current observations, so the red noise must be generated by an alternative process.

astro-ph.SR↗

arXiv2023

The Puzzling Structure of Solar Convection: Window into the Dynamo

The operation of the solar dynamo, with all of its remarkable spatio-temporal ordering, remains an outstanding problem of modern solar physics. A number of mechanisms that might plausibly contribute to its operation have been proposed, but the relative role played by each remains unclear. This uncertainty stems from continuing questions concerning the speed and structure of deep-seated convective flows. Those flows are in-turn thought to sustain both the Sun's turbulent EMF and the large-scale flows of differential rotation and meridional circulation suspected of influencing the dynamo's organization and timing. Continued progress in this area is complicated by (i) inconsistencies between helioseismic measurements of convective and meridional flow made with different techniques and instruments, and (ii) a lack of high-latitude data for convection, differential rotation, and meridional flow. We suggest that the path forward to resolving these difficulties is twofold. First, the acquisition of long-term helioseismic and emissivity measurements obtained from a polar vantage point is vital to complete our picture of the Sun's outer convection zone. Second, sustained and expanded investment in theory-oriented and combined theory/observational research initiatives will be crucial to fully exploit these new observations and to resolve inconsistencies between existing measurements.

astro-ph.SR↗

arXiv2022

The Stability of Prendergast Magnetic Fields

Convection in massive main sequence stars generates large scale magnetic fields in their cores which persists as they evolve up the red giant branch. The remnants of these fields may take the form of the Prendergast magnetic field, a combination of poloidal and toroidal field components which are expected to stabilize each other. Previous analytic and numerical calculations did not find any evidence for instability of the Prendergast field over short timescales. In this paper, we present numerical simulations which show a long timescale, linear instability of this magnetic field. We find the instability to be robust to changes in boundary conditions and it is not stabilized by strong stable stratification. The instability is a resistive instability, and the growth rate has a power-law dependence on the resistivity, in which the growth rate decreases as the resistivity decreases. We estimate the growth rate of the instability in stars by extrapolating this power-law to stellar values of the resistivity. The instability is sufficiently rapid to destabilize the magnetic field on timescales shorter than the stellar evolution timescale, indicating that the Prendergast field is not a good model to use in studies of magnetic fields in stars.

astro-ph.SR↗

arXiv2022

Moosinesq Convection in the Cores of Moosive Stars

Stars with masses $\gtrsim 4 \times 10^{27}M_{\rm{moose}} \approx 1.1 M_\odot$ have core convection zones during their time on the main sequence. In these moosive stars, convection introduces many uncertainties in stellar modeling. In this Letter, we build upon the Boussinesq approximation to present the first-ever simulations of Moosinesq convection, which captures the complex geometric structure of the convection zones of these stars. These flows are bounded in a manner informed by the majestic terrestrial Alces alces (moose) and could have important consequences for the evolution of these stars. We find that Moosinesq convection results in very interesting flow morphologies and rapid heat transfer, and posit this as a mechanism of biomechanical thermoregulation.

astro-ph.SR↗

arXiv2022

Stellar convective penetration: parameterized theory and dynamical simulations

Most stars host convection zones in which heat is transported directly by fluid motion, but the behavior of convective boundaries is not well understood. Here we present 3D numerical simulations which exhibit penetration zones: regions where the entire luminosity \emph{could} be carried by radiation, but where the temperature gradient is approximately adiabatic and convection is present. To parameterize this effect, we define the "penetration parameter" $\mathcal{P}$ which compares how far the radiative gradient deviates from the adiabatic gradient on either side of the Schwarzschild convective boundary. Following Roxburgh (1989) and Zahn (1991), we construct an energy-based theoretical model in which $\mathcal{P}$ controls the extent of penetration. We test this theory using 3D numerical simulations which employ a simplified Boussinesq model of stellar convection. The convection is driven by internal heating and we use a height-dependent radiative conductivity; this allows us to separately specify $\mathcal{P}$ and the stiffness $\mathcal{S}$ of the radiative-convective boundary. We find significant convective penetration in all simulations. Our simple theory describes the simulations well. Penetration zones can take thousands of overturn times to develop, so long simulations or accelerated evolutionary techniques are required. In stars, we expect $\mathcal{P} \approx 1$ and in this regime our results suggest that convection zones may extend beyond the Schwarzschild boundary by up to $\sim$20-30% of a mixing length. We present a MESA stellar model of the Sun which employs our parameterization of convective penetration as a proof of concept. We discuss prospects for extending these results to more realistic stellar contexts.

astro-ph.SR↗

arXiv2021

A Validated Nonlinear Kelvin-Helmholtz Benchmark for Numerical Hydrodynamics

The nonlinear evolution of the Kelvin-Helmholtz instability is a popular test for code verification. To date, most Kelvin-Helmholtz problems discussed in the literature are ill-posed: they do not converge to any single solution with increasing resolution. This precludes comparisons among different codes and severely limits the utility of the Kelvin-Helmholtz instability as a test problem. The lack of a reference solution has led various authors to assert the accuracy of their simulations based on ad-hoc proxies, e.g., the existence of small-scale structures. This paper proposes well-posed Kelvin-Helmholtz problems with smooth initial conditions and explicit diffusion. We show that in many cases numerical errors/noise can seed spurious small-scale structure in Kelvin-Helmholtz problems. We demonstrate convergence to a reference solution using both Athena, a Godunov code, and Dedalus, a pseudo-spectral code. Problems with constant initial density throughout the domain are relatively straightforward for both codes. However, problems with an initial density jump (which are the norm in astrophysical systems) exhibit rich behavior and are more computationally challenging. In the latter case, Athena simulations are prone to an instability of the inner rolled-up vortex; this instability is seeded by grid-scale errors introduced by the algorithm, and disappears as resolution increases. Both Athena and Dedalus exhibit late-time chaos. Inviscid simulations are riddled with extremely vigorous secondary instabilities which induce more mixing than simulations with explicit diffusion. Our results highlight the importance of running well-posed test problems with demonstrated convergence to a reference solution. To facilitate future comparisons, we include the resolved, converged solutions to the Kelvin-Helmholtz problems in this paper in machine-readable form.

astro-ph.IM↗

arXiv2020

Convective dynamics with mixed temperature boundary conditions: why thermal relaxation matters and how to accelerate it

Astrophysical simulations of convection frequently impose different thermal boundary conditions at the top and the bottom of the domain in an effort to more accurately model natural systems. In this work, we study Rayleigh-Benard convection (RBC) under the Boussinesq approximation. We examine simulations with mixed temperature boundary conditions in which the flux is fixed at the bottom boundary and the temperature is fixed at the top ("FT"). We aim to understand how FT boundaries change the nature of the convective solution compared to the traditional choice of thermal boundaries, in which the temperature is fixed at the top and bottom of the domain ("TT"). We demonstrate that the timescale of thermal relaxation for FT simulations is dependent upon the initial conditions. "Classic" initial conditions which employ a hydrostatically -- and thermally -- balanced linear temperature profile exhibit a long thermal relaxation. This long relaxation is not seen in FT simulations which use a TT simulation's nonlinear state as initial conditions ("TT-to-FT"). In the thermally relaxed, statistically stationary state, the mean behavior of an FT simulation corresponds to an equivalent simulation with TT boundaries, and time- and volume-averaged flow statistics like the Nusselt number and the Peclet number are indistinguishable between FT and TT simulations. FT boundaries are fundamentally asymmetric, and we examine the asymmetries that these boundaries produce in the flow. We find that the fixed-flux boundary produces more extreme temperature events than the fixed-temperature boundary. However, these near-boundary asymmetries do not measurably break the symmetry in the convective interior. We briefly explore rotating RBC to demonstrate that our findings with respect to thermal relaxation carry over to this more complex case, and to show the power of TT-to-FT initial conditions.

physics.flu-dyn↗

arXiv2020

Single-hemisphere dynamos in M-dwarf stars

M-dwarf stars below a certain mass are convective from their cores to their photospheres. These fully convective objects are extremely numerous, very magnetically active, and the likely hosts of many exoplanets. Here we study, for the first time, dynamo action in simulations of stratified, rotating fully convective M-dwarf stars. Importantly, we use new techniques to capture the correct full ball geometry down to the center of the star. We find surprising dynamo states in these systems, with the global-scale mean fields confined strongly to a single hemisphere, in contrast to prior stellar dynamo solutions. These hemispheric-dynamo stars are likely to have profoundly different interactions with their surroundings, with important implications for exoplanet habitability and stellar spindown.

astro-ph.SR↗

arXiv2019

The Magnetorotational Instability Prefers Three Dimensions

The magnetorotational instability (MRI) occurs when a weak magnetic field destabilises a rotating, electrically conducting fluid with inwardly increasing angular velocity. The MRI is essential to astrophysical disk theory where the shear is typically Keplerian. Internal shear layers in stars may also be MRI unstable, and they take a wide range of profiles, including near-critical. We show that the fastest growing modes of an ideal magnetofluid are three-dimensional provided the shear rate, $S$, is near the two-dimensional onset value, $S_c$. For a Keplerian shear, three-dimensional modes are unstable above $S\approx0.10S_c$, and dominate the two-dimensional modes until $S\approx2.05S_{c}$. These three-dimensional modes dominate for shear profiles relevant to stars and at magnetic Prandtl numbers relevant to liquid-metal laboratory experiments. Significant numbers of rapidly growing three-dimensional modes remain well past $2.05S_{c}$. These finding are significant in three ways. First, weakly nonlinear theory suggests that the MRI saturates by pushing the shear rate to its critical value. This can happen for systems, like stars and laboratory experiments, that can rearrange their angular velocity profiles. Second, the non-normal character and large transient growth of MRI modes should be important whenever three-dimensionality exists. Finally, three-dimensional growth suggests direct dynamo action driven from the linear instability.

physics.plasm-ph↗

arXiv2019

Dedalus: A Flexible Framework for Numerical Simulations with Spectral Methods

Numerical solutions of partial differential equations enable a broad range of scientific research. The Dedalus Project is a flexible, open-source, parallelized computational framework for solving general partial differential equations using spectral methods. Dedalus translates plain-text strings describing partial differential equations into efficient solvers. This paper details the numerical method that enables this translation, describes the design and implementation of the codebase, and illustrates its capabilities with a variety of example problems. The numerical method is a first-order generalized tau formulation that discretizes equations into banded matrices. This method is implemented with an object-oriented design. Classes for spectral bases and domains manage the discretization and automatic parallel distribution of variables. Discretized fields and mathematical operators are symbolically manipulated with a basic computer algebra system. Initial value, boundary value, and eigenvalue problems are efficiently solved using high-performance linear algebra, transform, and parallel communication libraries. Custom analysis outputs can also be specified in plain text and stored in self-describing portable formats. The performance of the code is evaluated with a parallel scaling benchmark and a comparison to a finite-volume code. The features and flexibility of the codebase are illustrated by solving several examples: the nonlinear Schrodinger equation on a graph, a supersonic magnetohydrodynamic vortex, quasigeostrophic flow, Stokes flow in a cylindrical annulus, normal modes of a radiative atmosphere, and diamagnetic levitation. The Dedalus code and the example problems are available online at http://dedalus-project.org/.

astro-ph.IM↗